Section 11.4: Evaluating Logarithms Worksheet 11.4
Great News!
Most of the time we use a calculator to evaluate logarithms! :D
Common Logarithms
Vocab: Base 10 logarithms are called common logarithms and we write
$$\log x$$
with the understanding that we mean $\log_{10} x.$
Example: Use your TI or Casio calculator to evaluate $\log 15.$
Natural Logarithms
More Vocab: Base $e$ logarithms are called natural logarithms and we write
$$\ln x$$
with the understanding that we mean $\log_{e} x.$
Example: Use your TI or Casio calculator to evaluate $\ln 5.$
Dire Warning: The notation we use in this class is not necessarily standard! D:
Some calculators only have the natural logarithmic key, which is very often
called LOG instead of LN, even though the base is e.
If you are unsure of the meaning of LOG on a particular calculator,
test a known value such as LOG 10 to determine which base is being used.
For example, we know $\log 10 = 1,$ but $\ln 10 \approx 2.30.$
Examples: Use your calculator to evaluate the following expressions
$\log 0.0001$
$\ln 0.33$
$\ln 77.1$
$\log 31.08$
$\log\left(4.82\times 10^{17}\right)$
$\ln\left(1.55\times 10^{-8}\right)$